97 Grand Cherokee Ltd. air conditioner does not stay cold.

Low on refrigerant, Have system checked for leaks. If no leaks, they will charge system and if all is well, you'll be cool.
Links below could be helpful

Everything You Need to Know About Your Car Completely Firestone Firestone...

How to Recharge Your Car Air Conditioner

Hello, There are a number of reasons that may cause your A/C to blow hot air. The compressor belt could be loose or broken, the A/C system could be low on freon, the A/C compressor clutch could be defective or the fuse could be blown, or the A/C mixing door could be stuck open just to name a few.

More they likely, low on freon, will need to do a leak test, to fine out where the leak is at, the reason the a/c compr, shut off, is the low pressure switch cut it off, when low on freon, that way the compr, wont get damage, or you could just keep recharging the a/c system.

if the compressor is turnning it could be you have developed a leak,or it could be that the air door which separates the heat from the ac is stuck open.vacume problem.if the compressor is not turnning it could be your low on freon,or an electrical issue.like a fuse or relay.

if it's not cold, then the refrigerant has leaked or it's low. A local shop can evacuate the system and check for leaks prior to filling with refrigerant. They can easily locate leaks in hoses, fittings, etc...
It's quite possible that there isn't any leaks ...it may be low on refrigerant, but it's best to check...saves $.

the refrigerant can be recoverd by the shop. discuss the cost with them and explain that you're going to do work yourself. and would like them to recover it, and once repairs are done, evacuate and charge the system. however, once the system is empty, i would replace the accumulator and orifice tube, or the receiver/dryer and expansion valve. which ever your car has. pag oil should also be added to the system. 2-4 oz should do. this can be done when re-charging.

do not rule out the blend door

Check the fuel pressure on it, clogged fuel filter, mass air flow sensor if it has it.

If you are loosing the freon you do have a leak.Your system will have to have a special dye shot into the system and then you need special glasses to see the dye.Ask a AC repair shop what they charge.

Well Bruno it sounds like you lost freon from your a/c system.The cabin filter wont restrict you from getting cold air.Check that your a/c clutch engages when you turn it on.if it dont you need freon and have to check for leaks

this is most likely a a lack of r-134a (as freon is no longer used), if your system is completely out or close to it then the pressure sensor will not allow the compressor clutch to engage, it is also possible that there is an electrical issue but less likely. to know for sure you need to put some gauges on the system